Traveling chimera pattern in a neuronal network under local gap and nonlocal coupling
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- 黑线是局部耦合，通过电紧张电位间隙链接到它的最近邻居。红虚线是非局部耦合，通过化学突触耦合到远的邻居节点。
module HR
implicit none
real,parameter :: h=0.01
integer,parameter :: N=100,MaxT=398700
integer,allocatable :: neighbour_matrix_2(:,:),neighbour_matrix_2P(:,:)
real :: x(N),y(N),z(N)
contains
subroutine x0_y0_z0()
implicit none
integer :: k
real :: x1,x2,x3
call random_seed()
do k=1,N,1
call random_number(x1)
call random_number(x2)
call random_number(x3)
x(k)=0.001*(k-N/2.0)+x1
y(k)=0.002*(k-N/2.0)+x2
z(k)=0.003*(k-N/2.0)+x3
write(10,*) x(k),y(k),z(k)
end do
end subroutine x0_y0_z0
subroutine fnf(p)
implicit none
integer :: i,j,p,t
real :: func_x(N),func_y(N),func_z(N),a,b,c,d,k1,k2,II,JJ,CC,r,s,x_R,v_s,lambda,thet_s
k1=0.0
k2=0.0
a=1.0
b=3.0
c=1.0
d=5.0
r=0.01
s=5.0
v_s=2.0
x_R=-1.6
lambda=10.0
thet_s=-0.25
II=0.0
do t=1,MaxT,1
if(mod(t,5000)==0) then
write(*,*) t
end if
do i=1,N,1
JJ=0.0
C=0.0
do j=1,N,1
JJ=JJ+neighbour_matrix_2(i,j)*(x(j)-x(i))
C=C+neighbour_matrix_2P(i,j)*(1.0/(1.0+exp(-lambda*(x(j)-thet_s))))
end do
func_x(i)=x(i)+h*(y(i)-a*x(i)**3+b*x(i)**2-z(i)+II+k1*JJ+((-k2/(2.0*p-2.0))*(v_s-x(i))*CC))
func_y(i)=y(i)+h*(c-d*x(i)**2-y(i))
func_z(i)=z(i)+h*(r*(s*(x(i)-x_R)-z(i)))
if(mod(t,50)==0.and.t>353700) then
write(20,*) i,t*h,x(i)
end if
if(i==1.and.t>353700) then
write(30,*) t*h,x(i)
write(70,*) x(i),y(i),z(i)
write(*,*) t*h,x(i)
end if
if(i==50.and.t>353700) then
write(40,*) t*h,x(i)
end if
end do
x=func_x
y=func_y
z=func_z
end do
return
end subroutine fnf
subroutine neighbour_2(K)
implicit none
integer :: K
integer :: i,j,number
allocate(neighbour_matrix_2(N,N))
neighbour_matrix_2=0
do i=1,N-1,1
do j=i+1,N,1
if(abs(i-j)<=K/2.or.abs(i-j)>=N-K/2) then
neighbour_matrix_2(i,j)=1
neighbour_matrix_2(j,i)=1
end if
end do
end do
do i=1,N,1
do j=1,N,1
write(50,"(I2)",advance='no') neighbour_matrix_2(i,j)
end do
write(50,*)
end do
return
end subroutine neighbour_2
subroutine neighbour_2P(K)
implicit none
integer :: K
integer :: i,j,number
allocate(neighbour_matrix_2P(N,N))
neighbour_matrix_2P=0
do i=1,N-1,1
do j=i+1,N,1
if((abs(i-j)<=K/2.or.abs(i-j)>=N-K/2).and.abs(i-j)/=1) then
neighbour_matrix_2P(i,j)=1
neighbour_matrix_2P(j,i)=1
end if
end do
end do
do i=1,N,1
do j=1,N,1
write(60,"(I2)",advance='no') neighbour_matrix_2P(i,j)
end do
write(60,*)
end do
return
end subroutine neighbour_2P
end module HR
program main
use HR
implicit none
integer :: p
p=40
open(10,file="data_x0_y0_z0.txt")
open(20,file="data_i_t_x.txt")
open(30,file="data_t_x5.txt")
open(40,file="data_t_x50.txt")
open(50,file="neighbour_matrix_2.txt")
open(60,file="neighbour_matrix_2P.txt")
open(70,file="x.txt")
call x0_y0_z0()
call neighbour_2(2)
call neighbour_2P(2*p+2)
call fnf(p)
deallocate(neighbour_matrix_2)
deallocate(neighbour_matrix_2P)
close(10)
close(20)
close(30)
close(40)
close(50)
close(60)
close(70)
end program main
module HR
implicit none
real,parameter :: h=0.005
integer,parameter :: MaxT=800000
real :: x,y,z
contains
subroutine x0_y0_z0()
implicit none
call random_seed()
call random_number(x)
call random_number(y)
call random_number(z)
end subroutine x0_y0_z0
subroutine fnf()
implicit none
integer :: t
real :: func_x,func_y,func_z,a,b,c,d,r,s,x_R,II
a=1.0
b=3.0
c=1.0
d=5.0
r=0.01
s=5.0
x_R=-1.6
II=3.8
do t=1,MaxT,1
if(mod(t,5000)==0) then
write(*,*) t
end if
func_x=x+h*(y-a*x**3+b*x**2-z+II)
func_y=y+h*(c-d*x**2-y)
func_z=z+h*(r*(s*(x-x_R)-z))
x=func_x
y=func_y
z=func_z
if(t>353700) then
write(30,*) t*h,x
write(*,*) t*h,x
end if
end do
return
end subroutine fnf
end module HR
program main
use HR
implicit none
open(10,file="data_x0_y0_z0.txt")
open(20,file="data_i_t_x.txt")
open(30,file="data_t_x.txt")
call x0_y0_z0()
call fnf()
close(10)
close(20)
close(30)
close(40)
end program main
module HR
implicit none
real,parameter :: h=0.01
integer,parameter :: N=100,MaxT=400000
integer,allocatable :: neighbour_matrix_2(:,:),neighbour_matrix_2P(:,:)
real :: x(N),y(N),z(N)
contains
subroutine x0_y0_z0()
implicit none
integer :: k
real :: x1,x2,x3
call random_seed()
do k=1,N,1
call random_number(x1)
call random_number(x2)
call random_number(x3)
x(k)=0.001*(k-N/2.0)+x1
y(k)=0.002*(k-N/2.0)+x2
z(k)=0.003*(k-N/2.0)+x3
write(10,*) x(k),y(k),z(k)
end do
end subroutine x0_y0_z0
subroutine fnf(p)
implicit none
integer :: i,j,p,t
real :: func_x(N),func_y(N),func_z(N),a,b,c,d,k1,k2,II,JJ,CC,r,s,x_R,v_s,lambda,thet_s
k1=3.0
k2=2.0
a=1.0
b=3.0
c=1.0
d=5.0
r=0.01
s=5.0
v_s=2.0
x_R=-1.6
lambda=10.0
thet_s=-0.25
II=3.8
do t=1,MaxT,1
if(mod(t,5000)==0) then
write(*,*) t
end if
do i=1,N,1
JJ=0.0
CC=0.0
do j=1,N,1
JJ=JJ+neighbour_matrix_2(i,j)*(x(j)-x(i))
CC=CC+neighbour_matrix_2P(i,j)*(1.0/(1.0+exp(-lambda*(x(j)-thet_s))))
end do
func_x(i)=x(i)+h*(y(i)-a*x(i)**3+b*x(i)**2-z(i)+II+k1*JJ+((-k2/(2.0*p-2.0))*(v_s-x(i))*CC))
func_y(i)=y(i)+h*(c-d*x(i)**2-y(i))
func_z(i)=z(i)+h*(r*(s*(x(i)-x_R)-z(i)))
if(mod(t,50)==0.and.t>300000) then
write(20,*) i,t*h,x(i)
end if
if(i==1.and.t>350000) then
write(30,*) t*h,x(i)
write(*,*) t*h,x(i)
end if
if(t==350000) then
write(40,*) i,x(i)
end if
if(t==400000) then
write(50,*) i,x(i)
end if
end do
x=func_x
y=func_y
z=func_z
end do
return
end subroutine fnf
subroutine neighbour_2(K)
implicit none
integer :: K
integer :: i,j,number
allocate(neighbour_matrix_2(N,N))
neighbour_matrix_2=0
do i=1,N-1,1
do j=i+1,N,1
if(abs(i-j)<=K/2.or.abs(i-j)>=N-K/2) then
neighbour_matrix_2(i,j)=1
neighbour_matrix_2(j,i)=1
end if
end do
end do
return
end subroutine neighbour_2
subroutine neighbour_2P(K)
implicit none
integer :: K
integer :: i,j,number
allocate(neighbour_matrix_2P(N,N))
neighbour_matrix_2P=0
do i=1,N-1,1
do j=i+1,N,1
if((abs(i-j)<=K/2.or.abs(i-j)>=N-K/2).and.abs(i-j)/=1) then
neighbour_matrix_2P(i,j)=1
neighbour_matrix_2P(j,i)=1
end if
end do
end do
return
end subroutine neighbour_2P
end module HR
program main
use HR
implicit none
integer :: p
p=40
open(10,file="data_x0_y0_z0.txt")
open(20,file="data_i_t_x.txt")
open(30,file="data_t_x5.txt")
open(40,file="i_x1.txt")
open(50,file="i_x2.txt")
call x0_y0_z0()
call neighbour_2(2)
call neighbour_2P(2*p+2)
call fnf(p)
deallocate(neighbour_matrix_2)
deallocate(neighbour_matrix_2P)
close(10)
close(20)
close(30)
close(40)
close(50)
end program main
module HR
implicit none
real,parameter :: h=0.01
integer,parameter :: N=100,MaxT=400000
integer,allocatable :: neighbour_matrix_2(:,:),neighbour_matrix_2P(:,:)
real :: x(N),y(N),z(N)
contains
subroutine x0_y0_z0()
implicit none
integer :: k
real :: x1,x2,x3
call random_seed()
do k=1,N,1
call random_number(x1)
call random_number(x2)
call random_number(x3)
x(k)=0.001*(k-N/2.0)+x1
y(k)=0.002*(k-N/2.0)+x2
z(k)=0.003*(k-N/2.0)+x3
write(10,*) x(k),y(k),z(k)
end do
end subroutine x0_y0_z0
subroutine fnf(p)
implicit none
integer :: i,j,p,t
real :: func_x(N),func_y(N),func_z(N),a,b,c,d,k1,k2,II,JJ,CC,r,s,x_R,v_s,lambda,thet_s
k1=3.0
k2=4.0
a=1.0
b=3.0
c=1.0
d=5.0
r=0.01
s=5.0
v_s=2.0
x_R=-1.6
lambda=10.0
thet_s=-0.25
II=4.0
do t=1,MaxT,1
if(mod(t,5000)==0) then
write(*,*) t
end if
do i=1,N,1
JJ=0.0
CC=0.0
do j=1,N,1
JJ=JJ+neighbour_matrix_2(i,j)*(x(j)-x(i))
CC=CC+neighbour_matrix_2P(i,j)*(1.0/(1.0+exp(-lambda*(x(j)-thet_s))))
end do
func_x(i)=x(i)+h*(y(i)-a*x(i)**3+b*x(i)**2-z(i)+II+k1*JJ+((-k2/(2.0*p-2.0))*(v_s-x(i))*CC))
func_y(i)=y(i)+h*(c-d*x(i)**2-y(i))
func_z(i)=z(i)+h*(r*(s*(x(i)-x_R)-z(i)))
if(mod(t,50)==0.and.t>300000) then
write(20,*) i,t*h,x(i)
end if
if(i==1.and.t>350000) then
write(30,*) t*h,x(i)
write(*,*) t*h,x(i)
end if
if(t==350000) then
write(40,*) i,x(i)
end if
if(t==400000) then
write(50,*) i,x(i)
end if
end do
x=func_x
y=func_y
z=func_z
end do
return
end subroutine fnf
subroutine neighbour_2(K)
implicit none
integer :: K
integer :: i,j,number
allocate(neighbour_matrix_2(N,N))
neighbour_matrix_2=0
do i=1,N-1,1
do j=i+1,N,1
if(abs(i-j)<=K/2.or.abs(i-j)>=N-K/2) then
neighbour_matrix_2(i,j)=1
neighbour_matrix_2(j,i)=1
end if
end do
end do
return
end subroutine neighbour_2
subroutine neighbour_2P(K)
implicit none
integer :: K
integer :: i,j,number
allocate(neighbour_matrix_2P(N,N))
neighbour_matrix_2P=0
do i=1,N-1,1
do j=i+1,N,1
if((abs(i-j)<=K/2.or.abs(i-j)>=N-K/2).and.abs(i-j)/=1) then
neighbour_matrix_2P(i,j)=1
neighbour_matrix_2P(j,i)=1
end if
end do
end do
return
end subroutine neighbour_2P
end module HR
program main
use HR
implicit none
integer :: p
p=40
open(10,file="data_x0_y0_z0.txt")
open(20,file="data_i_t_x.txt")
open(30,file="data_t_x5.txt")
open(40,file="i_x1.txt")
open(50,file="i_x2.txt")
call x0_y0_z0()
call neighbour_2(2)
call neighbour_2P(2*p+2)
call fnf(p)
deallocate(neighbour_matrix_2)
deallocate(neighbour_matrix_2P)
close(10)
close(20)
close(30)
close(40)
close(50)
end program main
